Pre-lab Preparation Sheet for Experiment #15: Elasticity 1. Does equation 5.16 i

Question

Pre-lab Preparation Sheet for Experiment #15: Elasticity 1. Does equation 5.16 in the textbook agree with or contradict equation 94? Explain your answer 2. When it is not under stress, a certain couch cushion is 8 cm thick. a) When it is compressed by a 12-N force, it is 7 cm thick. What value of x describes this situation? b) If Hooke's law describes the cushion, what is its spring constant? c) How thick will the cushion then be when it is compressed by a 96-N force? d) What thickness does Hooke's law predict when the cushion is compressed by a 108- force? e) Does Hooke's law describe the cushion for such a force? Explain your answer. 3. Does Hooke's law describe the flexible object in textbook Figure 5.29(b)? Does Hooke's law describe the flexible object in textbook Figure 5.31(a)? - Does Hooke's law describe the flexible object in textbook Figure 9.8?

Explanation / Answer

2] According to Hooke's law, the restoring force produced due to the spring has magnitude:

F = kx

where k is the spring's constant and x is the displacement.

a] The compression here is:

x = 8 - 7 = 1 cm = 0.01 m.

b] F = 12 N

x = 0.01 m

therefore, k = F/x = 12/0.01 = 1200 N/m

c] If F = 96 N

x = F/k = 96/1200 = 0.08 m = 8 cm

that is, the spring is fully compressed.

So, the cushion will be 0 cm thick.

d] If F = 108 N

x = 108/1200 = 0.09 m = 9 cm

which is not possible since the initial thickness is itself 8 cm in length.

e] This situation is not described by Hooke's law as the displacement is more than the uncompressed length of the cushion.

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